臺灣博碩士論文加值系統

在影像估測或重組的問題上，如果量測數據無法完整地覆蓋所對映的傅立葉空間，正確地重組影像將是非常困難的事。以數學的觀點來看，將會造成無限多數據一致(Data Consistent)的答案存在，這樣通常無法決定一個擁有高解析度的影像結果。為此，可利用先備離散傅立葉轉換演算法(Prior Discrete Fourier Transform, PDFT)來解決此類非唯一性(Non-uniqueness)的問題。
先備離散傅立葉演算法是一種線性頻譜估測的技術，主要是利用有關原始物體的先備函數以改善影像品質。目前為止，先備離散傅立葉轉換演算法已獲得證明確實擁有改善影像解析度及精確度的能力。在先備離散傅立葉轉換演算法的應用上，如果先備函數的覆蓋範圍愈接近被估測物體的支援範圍(Support Domain)，其估測結果將擁有更高的解析度。但是假使物體的支援範圍過於不規則或複雜，一個好的先備函數通常不容易去決定。因此，一個能夠更精確決定先備函數的方法是非常重要的。在本論文中，主要針對此問題來研究，可發現利用間接先備離散傅立葉轉換演算法(Indirect Prior Discrete Fourier Transform, IPDFT)可以解決這個棘手的問題。
間接先備離散傅立葉轉換演算法的優點是即使在涵蓋範圍不好的情況下，依然可以準確地估測出物體的邊界。利用間接先備離散傅立葉轉換演算法準確地偵測出物體的輪廓，進一步決定更精確的先備函數，如此一來，便可以將其精確的輪廓應用於先備離散傅立葉轉換演算法去提升影像的解析度及精確度。

In image estimation or reconstruction, it is difficult to specify a unique and accurate solution if the coverage of available data is incomplete on the Fourier domain. From mathematical point of view, there will be infinitely many data-consistent solutions and one can not determine a high-resolution image typically. For this, we have been using the prior discrete Fourier transform (PDFT) to overcome this non-uniqueness problem.
The PDFT is a linear spectral estimation, which can use the prior knowledge about the object to be reconstructed to improve the resolution. The PDFT has been proved its great potential in the resolution enhancement. In the PDFT, a prior having its support closer to the object’s domain can provide a higher-resolution PDFT estimate. This technique is typically used to optimize the resolution, while it is not applicable when the object’s profile is complicated. In this dissertation, we concentrate on applying the indirect PDFT (IPDFT) to solve this problem.
The IPDFT can provide the accurate boundary information of the object being reconstructed even with a set poor-coverage data. With the accurate detection of the object’s boundaries, we can provide the PDFT an optimal prior function to increase the resolution.

摘要 i
Abstract iii
誌謝 v
目錄 vi
圖目錄 viii
第一章 序論 1
1.1 研究動機 1
1.2 研究方法 2
1.3 論文架構 3
第二章 先備離散傅立葉轉換 5
2.1 概述 5
2.2 數學模型 5
2.3 正規化法 11
2.4 選擇合適的先備函數 15
第三章 間接先備離散傅立葉轉換 23
3.1 概述 23
3.2 數學模型 24
3.2.1 維納濾波器 24
3.2.1.1 向量維納濾波器 27
3.2.1.2 有限脈衝響應維納濾波器 30
3.2.2 伯格最大熵法 32
3.2.3 間接離散傅立葉轉換演算法 34
3.3 二度空間的影像模擬 38
第四章 結合間接與直接先備離散傅立葉轉換之應用 42
4.1 概述 42
4.2 二度空間的影像模擬 43
4.3 間接先備離散傅立葉轉換於二度空間問題的適用性 49
第五章 結論 55
參考文獻 57

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